For the purpose of our questions you can put
together the 28 dominoes (pieces) in two type of arrangements:

Arrangement A (just showing 3 pieces):

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to produce one number as concatenations of all the
numbers

Arrangement B (just showing 3 pieces)

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to produce two numbers, one number as a concatenations
of all the numbers of the superior row and the other number as a
concatenation of all the numbers of the inferior row.

Questions:

1. Get the largest
prime number possible P, using the most of the 28 pieces according to
arrangement A, without worrying for any matching between contiguous pieces
(as in the normal domino game)

2. Redo the exercise 1 keeping the
matching between contiguous pieces as in the normal domino game.

3. Redo exercises 1 & 2 getting
the least
prime numbers.

4. Get the largest
two prime numbers P1 & P2, using the 28 pieces according to the
arrangement B, such that (P1-P2) is minimal

5. Redo the exercise 4 getting the least
two prime numbers
P1 & P2, using the 28 pieces according to the
arrangement B, such that (P1-P2) is minimal

Solution

Jeff Burch sent (June 4, 2000) the following solution to
question 1:

"Using all 28 dominos won't yield a prime number because the
sum of all numbers on all the dominoes is 168. All numbers like this
will be divisible by 3. Using 27 dominos, omitting the one with one zero
and one one the largest prime in problem #1 is 666564636261605554535251504443424140333231302220120011...In
the Maple V Release 4 program the isprime function when tested
with this number returns 'true'. This means the number is prime"

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Jeff Heleen, found (16/06/2000) another solution to question 1
but using another version of Domino:

"...Some domino sets have 55 tiles, going up to double nines. Using a set like this, the largest prime (for question 1) I have found so far is:

omitting only the 0/1 tile...I produced it by trial and error, switching tiles at the end, till one turned up prime. I used UBASIC's ECM to test it."

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Giuliano Daddario sent (22/8/01)the following
solution to question 3.1:

000102030405061112131415162223242526333435444555566663

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Later (26/8/2001) he sent his solution to the question
3.2:

the least prime number possible P, using the most of the 28 pieces
according to arrangement A, keeping the matching between contiguous
pieces as in the normal domino game is (eliminating only the piece 0-1)

000221111330044115522223333442266335555444466005566661

I would explain my line of reasoning about puzzle 94. Using all
the 28 pieces, if the number starts with the piece 0-0, it has to
terminate with a piece like A-0 (otherwise one of the zeroes is
unmatched). Now we have to eliminate a piece like X-0 or 0-X (otherwise
we have to put one zero in last position, and the number is not prime).
After the elimination, to guarantee the matching of all the
"X", the last digit has to be X. So, X=1 and you have to
eliminate the piece 0-1 (we can't eliminate the piece 0-3, because in
that case the number is divisible by 3).